An information-spectrum approach to source coding theorems with a fidelity criterion

The rate-distortion problem for the general class of nonstationary and/or nonergodic sources with an arbitrary distortion measure (not necessarily additive) is studied. We are especially concerned with the case of variable-rate coding under maximum-distortion criterion. It turns out that, in the framework where we cannot readily invoke the standard asymptotic equipartition property, an information-spectrum approach devised by Han and Verdu (1993) plays the key role in establishing such a general formula. Comparisons with the rate-distortion formulas with fixed-rate coding of Steinberg and Verdu (see ibid., vol.42, no.1, p.63-86, 1996) are also discussed to obtain an insight into the general features of this kind of nonstationary and nonergodic problems.